3. Results
Mean deep w’ variances for all 10070 profiles (computed from 1000 dbar to their deepest gridded pressure, at least 2995 dbar, typically within ~45 dbar of the seafloor) have an average value of 0.23 (±0.16) × 10-4 dbar-2s-2. However, the mean deep w’ variances are not normally distributed (Figure 3a), with 3% of the values falling below the mean minus one standard deviation and 10% of the values falling above the mean plus one standard deviation. The median value of 0.20 × 10-4 dbar-2s-2 is somewhat less than the mean value. The mean value corresponds to an idealized sinusoidal disturbance for w’over the entire pressure range with an amplitude of 0.007 dbar s-1. The largest local amplitudes of w’generally do not exceed 0.02 dbar s-1. Hence, the example shown (Figure 2) exhibits a signal with an amplitude towards the high end of the distribution.
The vertical wavelengths of w’ at the maximum power of thew’ Morlet wavelet spectrum, hereafter referred to as the dominant vertical wavelengths, (e.g., Figure 3b) have an average value of 890 (±290) dbar. Half of these values are 786 dbar or less, with less than 1% falling below 393 dbar, and half are 935 dbar or greater, with 6% at the maximum possible value of 1572 dbar. This distribution should be regarded with some caution, both because of potential biases resulting from slow profiling through propagating waves noted in the discussion section and because a segment 2.7 times the vertical wavelength is required for that wavelength to be free of the cone of influence (where zero-padding effects bias the power spectrum) even at the mid-point of the portion of the profile analyzed. Using the 46% of the profiles that extend to at least 5250 dbar, and hence can resolve a maximum vertical wavelength of 1572 dbar at their mid-point, results in an average value of 970 (±300) dbar for the dominant vertical wavelengths. This increase in wavelength is only 9% over the average value using the entire data set.
The geographic distributions of mean deep w’ variances (Figure 4) and dominant vertical wavelengths (Figure 5) both exhibit physically sensible patterns among basins and within some individual basins.
The mean deep w’ variances (Figure 4) are generally lower than average for the profiles in the North American Basin of the western North Atlantic Ocean, with a few higher values adjacent to the Caribbean Islands. Offshore, the abyssal plain there is very smooth and so these low variances might be anticipated. The dominant vertical wavelengths there are noticeably longer than average (Figure 5). These two features are consistent with little local generation or scattering of internal waves at rough topographic features and propagation of internal waves generated elsewhere from a long distance. The internal wave energy level in regions with little local generation would be expected to be lower, even for the longer vertical wavelength packets that survive traveling from remote generation regions. The few bins with higher variances and smaller wavelengths near the continental slope may result from local interactions between currents and the bathymetry there.
In the Brazil Basin of the western South Atlantic deep w’ variance values are largest and vertical wavelengths the smallest near the internal wave generation sites along the rough topography of the Mid-Atlantic Ridge. In contrast, over the smoother abyssal plain in the west far from internal wave generation regions the mean w’ variance values are lower and the vertical wavelengths are longer, suggesting that there are very few locally generated internal waves, leaving only low-mode internal waves that may have been generated elsewhere. This pattern is consistent with previous observations of a ridge-to-basin gradient in mixing in the Brazil Basin (Polzin et al., 1997) and with strain and shear variances from WOCE section data in many basins (Kunze et al., 2006). Further west, approaching the continental slope, wavelengths become shorter while the variance remains small, suggesting that while there is little local generation, the continental slope may be reflecting or scattering internal waves, a pattern consistent with modeling studies of the internal wave lifecycle (e.g., de Lavergne et al., 2019). The shorter wavelengths near the slope could also arise at least partly owing to the shorter profiles taken there not resolving the energy at longer wavelengths. In the Argentine Basin vertical wavelengths are small and the deep w’ variance is moderate to strong, consistent with the deep-reaching eddies and currents in the region (e.g., Fu, 2007) interacting with the internal wave field in a variety of ways including acting as a conduit for surface-generated internal waves (Danioux et al., 2008; Kunze, 1985; Young & BenJelloul, 1997), or causing a substantial reduction in the internal wave length scales via interactions with the currents vorticity or horizontal strain (Fer et al., 2018; Kunze, 1995).
The mean deep w’ variances (Figure 4) in the South Australian and Australian-Antarctic basins of the far eastern Indian Ocean are generally lower than average, especially in smooth regions of the basins, with some high values and shorter dominant vertical wavelengths (Figure 5) closer to topographic features. Just to the east, profiles south of the Campbell Plateau in the South Pacific have relatively high mean deep w’ variances and a variety of dominant vertical wavelengths. The deep-reaching Antarctic Circumpolar Current flows eastward through this region after transiting some very rough bathymetry to the west. Deep-reaching meanders and eddies of that current generating lee waves when flowing over that topography (Cusack et al., 2017; Waterman et al., 2013) may be responsible for some of those high variances.
In the Southwest Pacific Basin, mean deep w’ variances (Figure 4) are close to average in many locations, with higher values adjacent to the steep bathymetry of the Tonga-Kermadec Ridge and Trench system and around regions with rough bathymetry including the chain of seamounts comprising the Louisville Ridge. The lower variances to the north of that ridge in the center of the basin are in a region of smoother bathymetry, and again the dominant vertical wavelengths (Figure 5) tend to be longer there, consistent with propagation from remote forcing areas of most internal waves and weaker mixing found in that region.
Moving northward in the Pacific, mean deep w’ variances (Figure 4) are substantially higher than average within and immediately north of the Samoan Passage and in the Penrhyn Basin east of the Manihiki Plateau. The Samoan Passage is a constriction for northward flow of bottom water into the rest of the Pacific, with hydraulic jumps and strong mixing observed locally (Carter et al., 2019). The high values continuing farther to the north of the Passage and east of the Manihiki Plateau are perhaps partly owing to relatively rough bathymetry in those regions. Values are also high for the few floats in the North Pacific, all of which are close to steep topography. Moving from South to North these floats are found in the Clarion-Clipperton Fracture Zone, around the Hawaiian Islands, and off the continental slope just west of San Diego.